EN|RU Volume 17, No 4, 2010, P. 18-31 UDC 519.716 S. S. Marchenkov The closure operator in many-valued logic based on functional equations Abstract: On the set of many-valued logic functions the FE-closure operator based on functional equations is introduced. It is proved that the FE-closure operator generates a finite classification on the set $P_k$ of $k$-valued logic functions for every $k\ge2$. It is established that the least class in this classification is the class $H_k$ of homogeneous functions. A series of corollaries about finite FE-generating sets in FE-closed classes are deduced. Bibliogr. 24. Keywords: many-valued logic function, functional equation, FE-closure operator. Marchenkov Sergei Seraphimovich 1 1. Lomonosov Moscow State University, Leninskie gory, 119991 Moscow, Russia e-mail: mathcyb@cs.msu.su © Sobolev Institute of Mathematics, 2015